04791nam 22007695 450 991029976090332120220412171759.03-319-12496-X10.1007/978-3-319-12496-4(CKB)3710000000321548(EBL)1966835(OCoLC)898892853(SSID)ssj0001408178(PQKBManifestationID)11797470(PQKBTitleCode)TC0001408178(PQKBWorkID)11346218(PQKB)10381786(DE-He213)978-3-319-12496-4(MiAaPQ)EBC1966835(PPN)183150481(EXLCZ)99371000000032154820141220d2015 u| 0engur|n|---|||||txtccrApproximation of stochastic invariant manifolds stochastic manifolds for nonlinear SPDEs I /by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang1st ed. 2015.Cham :Springer International Publishing :Imprint: Springer,2015.1 online resource (136 p.)SpringerBriefs in Mathematics,2191-8198Description based upon print version of record.3-319-12495-1 Includes bibliographical references and index.General Introduction -- Stochastic Invariant Manifolds: Background and Main Contributions -- Preliminaries -- Stochastic Evolution Equations -- Random Dynamical Systems -- Cohomologous Cocycles and Random Evolution Equations -- Linearized Stochastic Flow and Related Estimates -- Existence and Attraction Properties of Global Stochastic Invariant Manifolds -- Existence and Smoothness of Global Stochastic Invariant Manifolds -- Asymptotic Completeness of Stochastic Invariant Manifolds -- Local Stochastic Invariant Manifolds: Preparation to Critical Manifolds -- Local Stochastic Critical Manifolds: Existence and Approximation Formulas -- Standing Hypotheses -- Existence of Local Stochastic Critical Manifolds -- Approximation of Local Stochastic Critical Manifolds -- Proofs of Theorem 6.1 and Corollary 6.1 -- Approximation of Stochastic Hyperbolic Invariant Manifolds -- A Classical and Mild Solutions of the Transformed RPDE -- B Proof of Theorem 4.1 -- References.This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations  take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems.SpringerBriefs in Mathematics,2191-8198DynamicsErgodic theoryDifferential equations, PartialProbabilitiesDifferential equationsDynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XPartial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Ordinary Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12147Dynamics.Ergodic theory.Differential equations, Partial.Probabilities.Differential equations.Dynamical Systems and Ergodic Theory.Partial Differential Equations.Probability Theory and Stochastic Processes.Ordinary Differential Equations.510515.352515.353515.39Chekroun Mickaël Dauthttp://id.loc.gov/vocabulary/relators/aut768294Liu Honghuauthttp://id.loc.gov/vocabulary/relators/autWang Shouhongauthttp://id.loc.gov/vocabulary/relators/autBOOK9910299760903321Approximation of Stochastic Invariant Manifolds2499255UNINA